Semantics, Specification Logic, and Hoare Logic of Exact Real Computation
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| Publicado en: | arXiv.org (Jun 21, 2024), p. n/a |
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| Autor principal: | |
| Otros Autores: | , , , , , , , , |
| Publicado: |
Cornell University Library, arXiv.org
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| Materias: | |
| Acceso en línea: | Citation/Abstract Full text outside of ProQuest |
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| 001 | 2076424577 | ||
| 003 | UK-CbPIL | ||
| 022 | |a 2331-8422 | ||
| 024 | 7 | |a 10.46298/lmcs-20(2:17)2024 |2 doi | |
| 035 | |a 2076424577 | ||
| 045 | 0 | |b d20240621 | |
| 100 | 1 | |a Park, Sewon | |
| 245 | 1 | |a Semantics, Specification Logic, and Hoare Logic of Exact Real Computation | |
| 260 | |b Cornell University Library, arXiv.org |c Jun 21, 2024 | ||
| 513 | |a Working Paper | ||
| 520 | 3 | |a We propose a simple imperative programming language, ERC, that features arbitrary real numbers as primitive data type, exactly. Equipped with a denotational semantics, ERC provides a formal programming language-theoretic foundation to the algorithmic processing of real numbers. In order to capture multi-valuedness, which is well-known to be essential to real number computation, we use a Plotkin powerdomain and make our programming language semantics computable and complete: all and only real functions computable in computable analysis can be realized in ERC. The base programming language supports real arithmetic as well as implicit limits; expansions support additional primitive operations (such as a user-defined exponential function). By restricting integers to Presburger arithmetic and real coercion to the `precision' embedding \(\mathbb{Z}\ni p\mapsto 2^p\in\mathbb{R}\), we arrive at a first-order theory which we prove to be decidable and model-complete. Based on said logic as specification language for preconditions and postconditions, we extend Hoare logic to a sound (w.r.t. the denotational semantics) and expressive system for deriving correct total correctness specifications. Various examples demonstrate the practicality and convenience of our language and the extended Hoare logic. | |
| 653 | |a Linear equations | ||
| 653 | |a Computation | ||
| 653 | |a Semantics | ||
| 653 | |a Mathematical models | ||
| 653 | |a Program verification (computers) | ||
| 653 | |a Floating structures | ||
| 653 | |a Integers | ||
| 653 | |a Rounding | ||
| 653 | |a Imperative programming | ||
| 653 | |a Floating point arithmetic | ||
| 653 | |a Programming languages | ||
| 700 | 1 | |a Brauße, Franz | |
| 700 | 1 | |a Collins, Pieter | |
| 700 | 1 | |a Kim, SunYoung | |
| 700 | 1 | |a Konečný, Michal | |
| 700 | 1 | |a Lee, Gyesik | |
| 700 | 1 | |a Müller, Norbert | |
| 700 | 1 | |a Neumann, Eike | |
| 700 | 1 | |a Preining, Norbert | |
| 700 | 1 | |a Ziegler, Martin | |
| 773 | 0 | |t arXiv.org |g (Jun 21, 2024), p. n/a | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/2076424577/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full text outside of ProQuest |u http://arxiv.org/abs/1608.05787 |